Answer
$\dfrac{3}{4}$
Work Step by Step
The total area of the triangle is: $\ Area = \dfrac{3}{2}$
Let us consider that
$Volume =\int_0^1 \int_0^{3x} x \ y \ dy \ dx $
or, $=\dfrac{1}{2} \int_0^1 x [y^2]_0^{3x} dx $
or, $=\dfrac{9}{2} \int_0^1 x^3 dx $
or, $Volume=\dfrac{9}{8} [ x^3]_0^1 dx =\dfrac{9}{8}$
The average value will be:
$V_{Av}= \dfrac{Total \ Volume}{Total \ Area}=\dfrac{9/8}{3/2} =\dfrac{3}{4}$
